Fixed points for multi-class queues

Burke's theorem can be seen as a fixed-point result for an exponential single-server queue; when the arrival process is Poisson, the departure process has the same distribution as the arrival process. We consider extensions of this result to multi-type queues, in which different types of customer have different levels of priority. We work with a model of a queueing server which includes discrete-time and continuous-time M/M/1 queues as well as queues with exponential or geometric service batches occurring in discrete time or at points of a Poisson process. The fixed-point results are proved using interchangeability properties for queues in tandem, which have previously been established for one-type M/M/1 systems. Some of the fixed-point results have previously been derived as a consequence of the construction of stationary distributions for multi-type interacting particle systems, and we explain the links between the two frameworks. The fixed points have interesting "clustering" properties for lower-priority customers. An extreme case is an example of a Brownian queue, in which lower-priority work only occurs at a set of times of measure 0 (and corresponds to a local time process for the queue-length process of higher priority work).Comment: 25 page

Decay of tails at equilibrium for FIFO join the shortest queue networks

In join the shortest queue networks, incoming jobs are assigned to the shortest queue from among a randomly chosen subset of $D$ queues, in a system of $N$ queues; after completion of service at its queue, a job leaves the network. We also assume that jobs arrive into the system according to a rate-$\alpha N$ Poisson process, $\alpha<1$, with rate-1 service at each queue. When the service at queues is exponentially distributed, it was shown in Vvedenskaya et al. [Probl. Inf. Transm. 32 (1996) 15-29] that the tail of the equilibrium queue size decays doubly exponentially in the limit as $N\rightarrow\infty$. This is a substantial improvement over the case D=1, where the queue size decays exponentially. The reasoning in [Probl. Inf. Transm. 32 (1996) 15-29] does not easily generalize to jobs with nonexponential service time distributions. A modularized program for treating general service time distributions was introduced in Bramson et al. [In Proc. ACM SIGMETRICS (2010) 275-286]. The program relies on an ansatz that asserts, in equilibrium, any fixed number of queues become independent of one another as $N\rightarrow\infty$. This ansatz was demonstrated in several settings in Bramson et al. [Queueing Syst. 71 (2012) 247-292], including for networks where the service discipline is FIFO and the service time distribution has a decreasing hazard rate. In this article, we investigate the limiting behavior, as $N\rightarrow \infty$, of the equilibrium at a queue when the service discipline is FIFO and the service time distribution has a power law with a given exponent $-\beta$, for $\beta>1$. We show under the above ansatz that, as $N\rightarrow\infty$, the tail of the equilibrium queue size exhibits a wide range of behavior depending on the relationship between $\beta$ and $D$. In particular, if $\beta>D/(D-1)$, the tail is doubly exponential and, if $\beta<D/(D-1)$, the tail has a power law. When $\beta=D/(D-1)$, the tail is exponentially distributed.Comment: Published in at http://dx.doi.org/10.1214/12-AAP888 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Transportation system reconstruction

2035-03-17 [Patent Duration]Current Assignees: Urban Engines Inc Google LLCA system for reconstructing vehicle itinerary include a processor and a memory storing instructions, implemented by the processor, to cluster historical trip records into a plurality of clusters, each of the plurality of clusters including a set of historical trip records that describe events occurring within a predetermined time range at one location; identify a sequence of clusters that includes a cluster at each location; and estimate an itinerary for a vehicle based on the sequence of clusters and constraint data describing physical constraints, the itinerary for the vehicle describing a sequence of arrival and departure times at a sequence of locations for the vehicle

Contemporary Information and Knowledge Management: Impact on Farming in India

Farming is an important part of Indian economy and it involves a wide range of stakeholders, of whom the small holder farmers are the largest group. Information sharing on new production processes with farmers was prominent in the ‘sixties which was key to the success of the Green Revolution. Agricultural extension, the process of enabling farmers and experts to exchange information with each other, has since been institutionalized to a high degree and is assessed to be not as effective as it had been a generation back. The advent of digital, technology-mediated information and knowledge management was thought to offer significant new opportunities for knowledge exchange in Indian farming as a whole. These hopes led to the launching of a number of initiatives in different parts of India, which has emerged as the host of the largest number of rural development projects where contemporary information and communication technology (ICT) play a pivotal role. While analyzing the outputs of such initiatives, many studies have pointed out that farming is not a priority concern of most of them. On the other hand, we can notice a non-complimentary strand of ICT in agriculture projects operated by a number of institutions with ICT resources playing a key role in some of them. These efforts, generally speaking, do not promote user participation in information flows quite unlike the contemporary trends